How do you use trigonometric substitution to write the algebraic expression #sqrt(x^2+100)# as a trigonometric function of #theta# where #0<theta<pi/2# and #x=10tantheta#?

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Answer 1 · 2018-05-19T03:12:43

#(Hypote)=sqrt[x^2+100]#

show below

#x=10tantheta#

#tantheta=x/10#

#tantheta=(Opposite)/(adjacent)#

from Pythagorean theorem in perpendicular triangle

#(Hypote)^2=(Opposite)^2+(adjacent)^2#

#(Hypote)^2=(x)^2+(10)^2=x^2+100#

#(Hypote)=sqrt[x^2+100]#